In how many different ways can the letters of the word 'GUINNESS' be arranged such that the vowels always come together?

Treat the four vowels (U, I, E, E) as a single connected unit to ensure they stay together, leaving the four consonants (G, N, N, S) as separate units. These 5 total units can be arranged among themselves in 5 factorial divided by 2 factorial ways due to the repeated N, which gives 60 ways. The vowels within their unit can be arranged in 4 factorial divided by 2 factorial ways due to the repeated E, giving 12 ways, and multiplying these gives 60 x 12 = 1080.

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